In dynamics music notation, piano is abbreviated 'p' and indicates that the music from that point on should be played softly. The word simply means "quiet" in Italian.
When added to the staff, it looks something like this (complete with eighth notes):
/\
---| /----------------------------------------------------
|/
---/---------------*---------*---------*---------*--------
/| | | | |
-/-|/\--------*---|-----*---|-----*---|-----*---|---------
| | | | | | | | | | |
|--|--|------|----|----|----|----|----|----|----|---------
\ | | |____|____|____|____|____|____|____|
--\|_/----------------------------------------------------
|
\| p